Determine all real numbers a for which the system of equations
\begin{align*}
3x^2+2y^2+2z^2&=a\\
4x^2+4y^2+5z^2&=1-a
\end{align*}
has at least one solution (x,y,z) in the real numbers. algebrasystem of equationsalgebra proposedquadratic equationparameterization